To continue ...
On 13 Jun 2008, at 14:37, Alan Hewat wrote:
Martin gives a good example for which interesting new information was
obtained from the PDF function - the fact that the Si-O bond lengths
do
not change during a structural transition in quartz.
But quartz is a rather special case. First of all quartz is simple
enough
that the Si-O distances might actually be measured directly from the
PDF -
this cannot often be the case.
Yes indeed, it is a special case. Which is really my point. In many
cases the "traditional" Rietveld approach is exactly what is needed.
Others may have different opinions, but in my view the overhead of
collecting and analysing total scattering data is too high for
anything other than the special cases. The special cases are more
common in our research than the name might suggest, but you might
expect that given the nature of research!
I realise that your special case point here concerns the simplicity of
the quartz structure. This is a valid point, but actually the short-
range distances can be understood for rather more complicated cases
than quartz. It is certainly the case though that PDF analysis will
run out of steam when even the short-range peaks overlap too much, but
fortunately lots of examples present interest science challenges
without this problem.
Second quartz is a material that exhibits strong librational motion of
small rigid units (associated with the transition) and unless such
libration is correctly modelled (using spherical harmonics in a
periodic
structural model) this is a textbook example of Rietveld refinement
under-estimating bond lengths by trying to fit a banana-shaped
distribution with an ellipsoid. With a correct model for libration you
would also obtain correct bond lengths by refinement from the Bragg
peaks
alone. As Martin says, "the Bragg peaks describe the average periodic
structure", which in this case consists of banana-shaped O-
distributions
at constant distance from Si.
Yes, this is true. Many materials though have these sorts of units, or
at least, many materials that give rise to interesting physical
phenomena such as negative thermal expansion and phase transitions do.
What I would comment on is that in such cases one should indeed do any
structure analysis with a proper single-atom distribution function,
such as a banana shape, rather than trying to force a standard thermal
ellipsoid model. However, my point is that this tells you one thing,
but it won't give you the pair distribution function, and for some
studies (the special cases) you might want scientific insight from the
pair distribution as well as (not instead of) the single-particle
distribution function.
Let's not quibble over whether the PDF and Patterson functions are the
same or not; in 1935 Patterson didn't have a computer and could only
measure Bragg peaks. What he described is the instantaneous electron
density folded with itself, which is precisely the definition of the
PDF
today. If you obtain this as he did by Fourier transforming the Bragg
intensities (F**2) you do ignore correlations that are non-periodic
with
the lattice, but he had no choice.
Much is made of "total scattering" implying that modulations in the
background bring essential new information to PDF not available to
Rietveld. "Total scattering" was in fact advocated for Rietveld
refinement
by Sabine 20+ years ago - see Young's book on the Rietveld method.
(Sabine
wrote the first neutron paper with Rietveld (Nature 1961) and coined
the
term Rietveld Refinement). A better example of the interest of
background
scattering might be anti-ferroelectric perovskite transitions
(Mike:-),
where atom displacements doubling the cell manifest as diffuse
scattering
between peaks.
Of course if we *define* Rietveld refinement as Bragg peak
refinement, we
restrict its power. I would define Rietveld refinement as direct
refinement of the structural parameters (atom positions etc) to fit
the
observed data (without first extracting structure factors or
performing
other intermediate operations, which was usual before Rietveld).
One indeed has to be very careful about semantics (or just 'names 'in
less subtle cases). If you define Patterson functions as only
involving the Bragg peaks, it is different from PDF. If you define
Patterson as from the whole pattern (including diffraction), then
indeed you formally have the PDF.
The one thing that I would stress about semantics concerns
understanding the difference between the information content of the
Bragg peaks and the information content of the Bragg + diffuse
scattering, ie the difference in the information content of long-range
order and short-range order. And I would stress that it is about
understanding the difference in information, and not about judging
whether one is better than the other. Where I think that the
differences are useful is when you can exploit both types of
information in your analysis.
I still think that Fourier transforming the total scattering, and then
refining against that, cannot do more than refining against the total
scattering directly. Martin almost says as much when he talks about
RMC.
The original question I think, was whether there is any computational
advantage in Fourier transforming the data before refining. Probably
not.
Alan is right here; the only difference maybe coming from whether
doing one or the other changes the weighting of the information you
are fitting against. I think that this is what Simon is arguing. One
difference is, as Simon points out, is that an understanding of the
PDF may be what you are after. Also as Simon points out, the RMC
approach to fitting does give you a particular focus on short-range
structure.
My main message is that crystallographers do have a choice of methods
now, but they are not equivalent in terms of effort or outcomes.
Best wishes
Martin
_______________________________________________
Martin Dove
Mineral Physics group, Department of Earth Sciences,
University of Cambridge, Downing Street, Cambridge CB2 3EQ
tel. 01223-333482 (office) 01223-711541 (home) 07889 724767 (mobile)
http://www.esc.cam.ac.uk/astaff/dove
